Uniqueness results of a nonlinear stochastic diffusion-convection equation with reflection

2025/04/04 by Niklas Sapountzoglou, Sapountzoglou, Niklas
Economics, Econometrics and Finance · Mathematics · #35K55 #35R35 #35R60 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2504.03417

openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in the uniqueness of solutions of a nonlinear, pseudomonotone, stochastic diffusion evolution problem with homogeneous Dirichlet boundary conditions with reflection, where the noise term is additive and given by a stochastic Itô integral with respect to a Hilbert space valued cylindrical Wiener process. In fact, since there is no Itô formula available for a solution in general, a general uniqueness result seems not to be available. Nevertheless, assuming more regularity for the solutions or the reflection, we may show some comparison principles.

Citations

• Stochastic pseudomonotone parabolic obstacle problem: well-posedness & Lewy-Stampacchia's inequalities
• Renormalized solutions of nonlinear parabolic equations with general measure data
• Les Inequations en Mecanique et en Physique

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